Problem: Which of the following numbers is a multiple of 13? ${43,57,75,116,117}$
Solution: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $43 \div 13 = 3\text{ R }4$ $57 \div 13 = 4\text{ R }5$ $75 \div 13 = 5\text{ R }10$ $116 \div 13 = 8\text{ R }12$ $117 \div 13 = 9$ The only answer choice that leaves no remainder after the division is $117$ $ 9$ $13$ $117$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $117$ $117 = 3\times3\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $117$. We can say that $117$ is divisible by $13$.